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Pi/Transcript
Transcript Text reads: The Mysteries of Life starring Tim and Moby Tim and Moby are standing in a sandbox. An animation shows Moby attempting to draw a circle in the sand. MOBY: Beep. TIM: You'll never get a perfect circle. People have gone crazy trying to do that. Tim reads from a typed letter. TIM: Dear Tim and Moby. what is pi, anyway? From Robin. Your question is one that ancient mathematicians and engineers puzzled over for thousands of years. An image shows a circle. A line is drawn around the circle. Text reads: circumference. An animation shows a line being drawn across the circle through its center. Text reads: diameter. TIM: They wanted to find the relationship between a perfect circle’s circumference and its diameter. That’s harder than it sounds — perfect circles in nature are hard to find, so pi can only be derived using theoretical equations. Tim tries to use a ruler to measure the distance across a slice of orange. TIM: So what is pi? It’s just a letter from the Greek alphabet used to represent the ratio between circumference and diameter. An image shows the symbol for pi. TIM: If you take a perfect circle of any size at all, and divide its circumference by its diameter you’ll get pi, or approximately 3.14. An image shows a circle. The circumference and diameter of the circle are highlighted. Equation reads: Startfraction circumference over diameter EndFraction equals 3.14. TIM: Actually, it’s 3.1415926535 ...and so on. The image for pi is shown. Behind pi, a non-terminating, non-repeating decimal is being written one digit at a time. TIM: It goes on like that forever, without stopping and without repeating. That’s why we use pi to represent it — there’s no way to write the actual number. An animation shows pi growing larger. TIM: Pi is an irrational number. That means it can be written only as a decimal, not a fraction. The decimal value of pi scrolls across the screen. TIM: Lots of people have the mistaken belief that pi can be written as 22/7, but that’s not true. Equation reads: 22 over 7 equals pi. The equation is crossed out. TIM: I bet you’ve used pi before, to measure circles. In your math textbook, the equation for a circle’s circumference usually reads c equals 2 pi r, where r is the radius of a circle. The radius is half of the diameter. An arrow is drawn from the center of a circle to the circle’s edge. Equation reads: c equals 2 times pi times r. TIM: So, if we take a circle that has a radius of 6 centimeters, we can find it’s circumference by plugging 6 into the equation. Equation reads: c equals 2 times pi times 6. TIM: We don’t need to be that accurate in this case, so let’s use 3.14 for pi. Equation reads: c equals 2 times 3.14 times 6. TIM: The circumference is 2 times 3.14 times 6. 37.68 centimeters. MOBY: Beep. TIM: That’s true. Since 3.14 is only an approximation of pi, a more accurate way to write the circumference is 12 pi. An animation shows the decimal, “3.14,” that is in the equation being replaced by pi. TIM: You can get the area of the circle by plugging its radius into the equation a equals pi r squared. Equation reads: a equals 3.14 times r squared. An image shows a filled-in circle. Equation now reads: a equals 3.14 times 36. TIM: Six squared is 36. Our area works out to about 113.04 square centimeters. That’s all there is to it. MOBY: Beep. TIM: What is it? Moby lifts his arm to show Tim the symbol for pi written on his arm. TIM: I hope that’s fake... Moby tries to rub the pi symbol off his hand, but it remains unchanged. Moby frowns. MOBY: Beep. TIM: Come on, I think we have some orange spray paint. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts